On the estimation of jump points in smooth curves
(1999) Annals of the Institute of Statistical Mathematics — Vol. 51, n° 2, p. 231-251 (1999)
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- Abstract
- Two-step methods are suggested for obtaining optimal performance in the problem of estimating jump points in smooth curves. The first step is based on a kernel-type diagnostic, and the second on local least-squares. In the case of a sample of size n the exact convergence rate is n(-1), rather than n(-1 + delta) (for some delta > 0) in the context of recent one-step methods based purely on kernels, or n(-1)(log n)(1 + delta) for recent techniques based on wavelets. Relatively mild assumptions are required of the error distribution. Under more stringent conditions the kernel-based step in our algorithm may be used by itself to produce an estimator with exact convergence rate n(-1)(log n)(1/2). Our techniques also enjoy good numerical performance, even in complex settings, and so offer a viable practical alternative to existing techniques, as well as providing theoretical optimality.
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Gijbels, I., Hall, P., & Kneip, A. (1999). On the estimation of jump points in smooth curves. Annals of the Institute of Statistical Mathematics, 51(2), 231-251. https://doi.org/10.1023/A:1003802007064 (Original work published 1999)